An infinite family of superintegrable Hamiltonians with reflection in the plane

Details An infinite family of superintegrable Hamiltonians with reflection in the plane An infinite family of superintegrable Hamiltonians with reflection in the plane

2011-08-25

arxiv.org/abs/1108.5208v1

Physics

Mathematical Physics

19 pages

Scientific paper

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.

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